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Home >> Decimal >> Decimal to Mixed Fraction >> Examples

Convert Decimal to Mixed Fraction : Solved Examples

Decimal Point Place Value of digits in decimals Expanded Form of Decimal Read Decimals Decimal Places
Decimal to Fraction Decimal to Mixed Fraction Decimal to Lowest Fractional form Decimal into Percentage Like Decimals
Unlike Decimals Difference Like & Unlike Decimals Comparing or Ordering Decimals Ascending Order of Decimals Descending Order of Decimals
Multiplication of Decimals Division of Decimals



Convert the following decimals into Mixed fraction

A) 3.75
B) 1.90
C) 18.18
D) 6.5
E) 1.625
A) 3.75

Solution: Follow the steps of conversion:
Step 1: Numerator of fraction is equal to decimal (without the decimal point) and we get: Numerator = 375

Step 2 : Find number of Decimal Place in the given decimal
Decimals Places = two (i.e. digit 7 and 5)

Step 3: Denominator of fraction is equal to 1 followed by as many number of zero as there are decimal place.

As calculated in step 2, there are two decimal place, so we will write two zeros next to digit 1 and we get:

Denominator = 100

Now, we know that: Fraction = Numerator
Denominator


Put the values of numerator and denominator from step 1 & Step 3 and we get:

Fraction = 375
100


Now we will convert this fraction into lowest form

Step 4: Find HCF of numerator and denominator of fraction (calculated above)

Fraction = 375
100


HCF of 375 and 100 = 25

Step 5: Divide both numerator and denominator by HCF and we get:
Fraction = 375 ÷ 25
100 ÷ 25


Solve the above division expression and we get:

Fraction = 15
4


Now to convert above calculated fraction into mixed fraction, follow the below steps:

Step 6: Divide Numerator by denominator of above calculated fraction i.e.

15
4


Step 7: Quotient will be Whole Number Part of Mixed Fraction.

so, Quotient = Whole number Part = 3 (calculated above)

Step 8: Remainder will be now be the Numerator of Mixed Fraction.

so, Remainder = Numerator = 3 (calculated above)

Step 9: Denominator remains same, as calculated in step 5.

So, denominator = 4 and we get:

Mixed Fraction = 3 3
4





Solution: Follow the steps of conversion:
Step 1: Numerator of fraction is equal to decimal (without the decimal point) and we get:

Numerator = 1.90

Step 2 : Find number of Decimal Place in the given decimal

Decimals Places = two (i.e. digit 9 and 0)

Step 3: Denominator of fraction is equal to 1 followed by as many number of zero as there are decimal place.

As calculated in step 2, there are two decimal places, so we will write two zeros next to digit 1 and we get:

Denominator = 100

Now, we know that: Fraction = Numerator
Denominator


Put the values of numerator and denominator from step 1 & Step 3 and we get:

Fraction = 190
100


Now we will convert this fraction into lowest form

Step 4: Find HCF of numerator and denominator of fraction (calculated above)

Fraction = 190
100


HCF of 190 and 100 = 10

Step 5: Divide both numerator and denominator by HCF and we get:
Fraction = 190 ÷ 10
100 ÷ 10


Solve the above division expression and we get:

Fraction = 19
10


Now to convert above calculated fraction into mixed fraction, follow the below steps:

Step 6: Divide Numerator by denominator of above calculated fraction i.e.

19
10


Step 7: Quotient will be Whole Number Part of Mixed Fraction.

so, Quotient = Whole number Part = 1 (calculated above)

Step 8: Remainder will be now be the Numerator of Mixed Fraction.

so, Remainder = Numerator = 9 (calculated above)

Step 9: Denominator remains same, as calculated in step 5.

So, denominator = 10 and we get:

Mixed Fraction = 1 9
10





C) 18.18

Solution: Follow the steps of conversion:

Step 1: Numerator of fraction is equal to decimal (without the decimal point) and we get:

Numerator = 18.18

Step 2 : Find number of Decimal Place in the given decimal

Decimals Places = two (i.e. digit 1 and 8)

Step 3: Denominator of fraction is equal to 1 followed by as many number of zero as there are decimal place.

As calculated in step 2, there are two decimal places, so we will write two zeros next to digit 1 and we get:

Denominator = 100

Now, we know that: Fraction = Numerator
Denominator


Put the values of numerator and denominator from step 1 & Step 3 and we get:

Fraction = 1818
100


Now we will convert this fraction into lowest form

Step 4: Find HCF of numerator and denominator of fraction (calculated above)

Fraction = 1818
100


HCF of 1818 and 100 = 2

Step 5: Divide both numerator and denominator by HCF and we get:
Fraction = 1818 ÷ 2
100 ÷ 2


Solve the above division expression and we get:

Fraction = 909
50


Now to convert above calculated fraction into mixed fraction, follow the below steps:

Step 6: Divide Numerator by denominator of above calculated fraction i.e.

909
50


Step 7: Quotient will be Whole Number Part of Mixed Fraction.

so, Quotient = Whole number Part = 18 (calculated above)

Step 8: Remainder will be now be the Numerator of Mixed Fraction.

so, Remainder = Numerator = 9 (calculated above)

Step 9: Denominator remains same, as calculated in step 5.

So, denominator = 50 and we get:

Mixed Fraction = 18 9
50





D) 6.5

Solution: Follow the steps of conversion:

Step 1: Numerator of fraction is equal to decimal (without the decimal point) and we get:

Numerator = 65

Step 2 : Find number of Decimal Place in the given decimal

Decimals Places = one only (i.e. digit 5)

Step 3: Denominator of fraction is equal to 1 followed by as many number of zero as there are decimal place.

As calculated in step 2, there is only one decimal place, so we will write one zero next to digit 1 and we get:

Denominator = 10

Now, we know that: Fraction = Numerator
Denominator


Put the values of numerator and denominator from step 1 & Step 3 and we get:

Fraction = 65
10


Now we will convert this fraction into lowest form

Step 4: Find HCF of numerator and denominator of fraction (calculated above)

Fraction = 65
10


HCF of 65 and 10 = 5

Step 5: Divide both numerator and denominator by HCF and we get:
Fraction = 65 ÷ 5
10 ÷ 5


Solve the above division expression and we get:

Fraction = 13
2


Now to convert above calculated fraction into mixed fraction, follow the below steps:

Step 6: Divide Numerator by denominator of above calculated fraction i.e.

13
2


Step 7: Quotient will be Whole Number Part of Mixed Fraction.

so, Quotient = Whole number Part = 6 (calculated above)

Step 8: Remainder will be now be the Numerator of Mixed Fraction.

so, Remainder = Numerator = 1 (calculated above)

Step 9: Denominator remains same, as calculated in step 5.

So, denominator = 2 and we get:

Mixed Fraction = 6 1
2





E) 1.625

Solution: Follow the steps of conversion:

Step 1: Numerator of fraction is equal to decimal (without the decimal point) and we get:

Numerator = 1625

Step 2 : Find number of Decimal Place in the given decimal

Decimals Places = three (i.e. digit 6, 2 and 5)

Step 3: Denominator of fraction is equal to 1 followed by as many number of zero as there are decimal place.

As calculated in step 2, there are three decimal places, so we will write three zeros next to digit 1 and we get:

Denominator = 1000

Now, we know that: Fraction = Numerator
Denominator


Put the values of numerator and denominator from step 1 & Step 3 and we get:

Fraction = 1625
1000


Now we will convert this fraction into lowest form

Step 4: Find HCF of numerator and denominator of fraction (calculated above)

Fraction = 1625
1000


HCF of 1625 and 1000 = 125

Step 5: Divide both numerator and denominator by HCF and we get:
Fraction = 1625 ÷ 125
1000 ÷ 125


Solve the above division expression and we get:

Fraction = 13
8


Now to convert above calculated fraction into mixed fraction, follow the below steps:

Step 6: Divide Numerator by denominator of above calculated fraction i.e.

13
8


Step 7: Quotient will be Whole Number Part of Mixed Fraction.

so, Quotient = Whole number Part = 1 (calculated above)

Step 8: Remainder will be now be the Numerator of Mixed Fraction.

so, Remainder = Numerator = 5 (calculated above)

Step 9: Denominator remains same, as calculated in step 5.

So, denominator = 8 and we get:

Mixed Fraction = 1 5
8




Related Question Examples

  • Convert the following decimals into Mixed fraction

    A) 3.75
    B) 1.90
    C) 18.18
    D) 6.5
    E) 1.625
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